Issue 73

D. Leonetti, Fracture and Structural Integrity, 73 (2025) 256-266; DOI: 10.3221/IGF-ESIS.73.17

fracture toughness verification may be necessary, which is ensured in terms of maximum allowable thickness, mainly depending on the steel grade. For components loaded in tension, independent of the steel grade or geometry, the design value of the applied tension force N Ed shall satisfy:

N N ,

 Ed

(1)

1.0

t Rd

where N t,Rd is the design tension resistance of the element, which in this case contains holes and is equal to the governing (lowest) resistance, either the design plastic resistance of the gross cross-section N pl,Rd , or the design ultimate resistance of the net cross section N u,Rd :

Af

y



N

(2)

pl Rd ,



M

0

A f

0.9

net u



N

(3)

u Rd ,



M

2

where A is the gross cross-sectional area, f y is the nominal value of the yield strength, fu is the characteristic value of the ultimate tensile strength, Anet is the net cross-section area, and γ M0 and γ M2 are partial factors. The EN 1993-1-12 [3] formulates the net cross-sectional resistance of steel plates of steel grade S460 up to S700 similar to the one presented in Eqn. 3, with the only difference being the substitution of γ M12 instead of γ M2 . However, this part of the Eurocode also recommends using the same value for γ M12 as for γ M2 , so γ M12 = γ M2 . When a structural element is required to fail in a predictable and controlled manner such that it warns before failure hence, when a capacity design is requested, the design plastic resistance of the gross cross-section should be lower than the ultimate resistance of the net cross-section at the hole: N pl,Rd < N u,Rd . For the calculation of the design ultimate resistance of the net cross-section, the factor 0.9 is based on tension tests and fracture mechanics safety assessments, as explained by Sedlacek et al. in the commentary on EN 1993 [6]. After omitting the partial safety factor, the resistance function is obtained:  u net u N A f 0.9 (4) The factor 0.9 has been the subject of study of multiple researchers, who aimed to investigate the applicability and conservatism of the design rule presented as in Eqn. 4. It should be noted that in other international standards such as AISC360 [7] in clause D2 do not include the factor 0.9 in the formulation of the resistance function. The factor 0.9 is based on test evaluations of bolted connections loaded in tension and the potential presence of cracks around the hole, potentially lowering the net cross-sectional resistance of the element. Rombouts et al. [8] investigated 28 specimens of steel grade S235 with different bolt configurations where the net cross-section failure is decisive over the gross cross sectional resistance. The conclusion of this research was that the additional safety value of 0.9 can be omitted, for both plates with and without bolts. Snijder et al. [9] investigated the net cross-sectional resistance of additional bolt-hole configurations for different steel grades, namely S235 and S460, by validating a finite element model with test results and subsequently using it to generate additional numerical results. They found that the current partial factor in Eqn. 3, γ M2 = γ M12 =1.25 in the Netherlands, is over-conservative and could be reduced to 1.05 as a combined factor for both factor 0.9 and partial factor. However, the study proposed to omit the factor of 0.9 and keep γ M2 as a partial factor. The applicability of the resistance formula with cracks present due to fatigue was investigated by Baarssen et al. [10]. The specimens used were made of S275 plates with a single hole at the center. Relatively short fatigue cracks, i.e. having a length < 1 mm were induced at the deepest point of the bolt hole by cyclically loading the plate whereafter, the ultimate load was obtained by tensile tests. The cracks near the bolt hole led to additional stress concentration, resulting in a lowered ultimate resistance as compared to the specimens without cracks. However, the rule of Eurocode 3 deemed applicable to the pre-cracked specimens. The applicability of the design rules presented in EN 1993-1-1 [1] for low temperature conditions (<0°C) has not been studied previously. As compared to these studies, we investigate the effect of relatively small cracks and the applicability of the resistance formula for specimens made of a high structural steel grade, namely S700MC, and by conducting tests on cooled specimens.

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